TY - JOUR T1 - A Stochastic Gradient Descent Approach for Stochastic Optimal Control AU - Archibald , Richard AU - Bao , Feng AU - Yong , Jiongmin JO - East Asian Journal on Applied Mathematics VL - 4 SP - 635 EP - 658 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.190420.200420 UR - https://global-sci.org/intro/article_detail/eajam/17944.html KW - Stochastic optimal control, stochastic gradient descent, maximum principle, forward backward stochastic differential equations. AB -

In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. The motivation that drives our method is the gradient of the cost functional in the stochastic optimal control problem is under expectation, and numerical calculation of such an expectation requires fully computation of a system of forward backward stochastic differential equations, which is computationally expensive. By evaluating the expectation with single-sample representation as suggested by the stochastic gradient descent type optimisation, we could save computational efforts in solving FBSDEs and only focus on the optimisation task which aims to determine the optimal control process.